jy3514953
幼苗
共回答了394个问题 举报
1/tanA+1/tanB=cosA/sinA+cosB/sinB
=(cosAsinB+sinAcosB)/(sinAsinB)
=sin(A+B)/(sinAsinB)=2sin(A+B)/(cos(A-B)-cos(A+B))
=2sinC/(cos(A-B)+cosC)
=2sin135/(cos(A-B)+cos135)
显然当A=B,cos(A-B)=1时上式取得最小值,此时
1/tanA+1/tanB=2sin135/(1+cos135)=2√2+2
1年前
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